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Calculus *BEST* Calculus 3 Textbook for self study

just to give a very simple test, can you define what it means for a function to be continuous at a point? or to be differentiable? can you define what it means to have a limit at a point? can you prove that the function f(x) = x^2 is continuous everywhere? can you prove that a function which is continuous everywhere on the interval [0,1] is bounded? can you define what it means for a function to be integrable on the interval [0,1]? can you prove that if f is a continuous function on [0,1], then the function F(x) = integral of f from 0 to x, is differentiable? can you define the exponential function and prove it is differentiable? Now you are getting some idea of what we discuss in my calculus class.
I have done all of those things previously in class and I know how to do them :)
Then demonstrate them now.
k give a problem to solve then and sorry if I sound cocky am trying not to be.

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